System for determining instability in an IIR filter

摘要

A digital transversal IIR filter, in which the sum of the magnitudes of a large number of coefficient multipliers (which may be real or complex) is greater than unity, may be stable or it may be unstable. The present invention is directed to (1) a test for stability in such a filter which is simpler and faster than solving a large number of polynomial equations, and (2) the repair of a filter found by this test to be unstable. Specifically, means responsive to the respective gradients of the magnitudes of chirp-z transforms of time-domain multiplier coefficient values within one or more selected localized regions of the complex in-phase (I), quadrature(Q) frequency-domain plane determine that a filter is unstable whenever the gradient of the magnitude values of the chirp-z transform within a selected localized region of the frequency-domain plane indicates that there is a pole in the frequency-domain plane that is located beyond the boundary of a frequency-domain unit circle. The selected localized region may consist of sample points situated on the respective circumferences of a unit circle, a slightly smaller circle inside the unit circle and a slightly larger circle outside the unit circle in the frequency domain plane. Repair of an unstable filter may be accomplished by deriving different non-zero valued multiplier coefficients by flattening the phase response within the selected localized region of the frequency domain before converting back to the time domain.